The Mary Selley is the perfect place to go if you want to eat well and eat cheap. It's next to one of the busy main streets of Bournemouth center, tours a corner and suddenly find yourself in a much more quiet, next to a beautiful church (where, among other people are buried Mary Shelley, author of Frankenstein). The pub has big windows. If you explore the menu you'll find some pretty good values. For less than 5 pounds you can eat well. The food is not bad and has some variety. Ideal to enjoy a traditional English breakfast, eat, have a beer or coffee. The staff is nice and if you're not fluent with English, many of the staff are Spanish. It has wi-fi network. This pub is part of a chain called Wetherspoon. All the pubs are exactly what you would find anywhere in the United Kingdom.
In the Triangle, Bournemouth, under the library. Comfortable, quirky and fun. The tables and seats are the most colorful (from airplane seats to beds). They have a variety food, coffees, teas, beers ... Not particularly cheap, but also not expensive. Dogs are more than welcome. The staff are very nice and many of the servers are Spanish and Latin, in case we have difficulty with the language. Wi-fi of course. They have some board games and a small football pitch where you can play for free. They even have blankets. It is, ultimately, a site made to spend a rainy afternoon long. Highly recommended, if only to see the décor.
Cozy place to have a meal in the heart of Bournemouth. The food is good, there is wi-fi and the park views are very nice. Not particularly expensive or cheap but highly recommend to go on Mondays, since throughout the day everything is half price. If you go on a Monday people can eat more than good for only 3 pounds. When I lived there I went every single Monday.
Beeeeeeest pizza all around UK and obviously Bournemouth!! It is very expensive but if you go on Tuesdays you pay half the price, so if you want to eat a traditional italian pizza outside Italy, go to BAFFI.